Does a laptop set the same resolution to a monitor like a desktop?

It depends on the graphics card but if the monitor uses standard resolution values then the laptop should set it the same way as your desktop. You should be able to manually set resolution though.

Nowadays

typically

any video display has a "fixed" resolution.

A particular make and model of desktop monitor will have a particular display resolution.

A particular make and model of laptop will have a particular display resolution.

There are some "standard resolutions" that MOST displays adopt

- basically: HDTV resolutions

but many displays do not adopt those standard resolutions.

A laptop

plugged into a desktop display

will normally recognize the desktop display and use the "native resolution" of the desktop display while it is connected to the desktop display.

Not if you want some other.  But most laptops can only do up to the same resolution as the internal panel.  You might set it to lower on an external monitor.

Some laptops have a discrete video chip besides the Intel or AMD CPU chip video out.

Then you can do a different and higher resolution than what is on the internal panel.

That is all that can be discussed about laptop and monitor resolutions without specific make and model.